Method of matched sections in application to thin-walled and Mindlin rectangular plates by Kirill Danylenko, Igor Orynyak

“… The paper elaborates the principally new variant of finite element method in application to plate problem. …”
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Two Numerical Methods for Solving the Schrödinger Parabolic and Pseudoparabolic Partial Differential Equations by Mahmut Modanli, Bushra Bajjah, Sevgi Kuşulay

“…The modified double Laplace decomposition method is applied to get the semianalytic solutions and the explicit finite difference method to get the approximate solutions of the problems. …”
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Simulation of Water Coning in Oil Reservoirs Using a Corrected IMPES Method

“…This method has no complexity compared to the fully implicit method, although both of them are based on the finite difference technique. …”
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Solving American Option Pricing Models by the Front Fixing Method: Numerical Analysis and Computing by R. Company, V. N. Egorova, L. Jódar

“…This paper presents an explicit finite-difference method for nonlinear partial differential equation appearing as a transformed Black-Scholes equation for American put option under logarithmic front fixing transformation. …”
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Stability analysis of a numerical method for the 3D high-order Allen–Cahn equation by Seokjun Ham, Jyoti, Jaeyong Choi, Yunjae Nam, Junseok Kim

“…We used a fully explicit Euler scheme for temporal derivatives and a second-order finite difference approach for spatial discretization. …”
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Structure-based modeling of artificial leather used in sports with non-symmetric fiber distribution by Tonghuan QU, Akihiro MATSUDA

“…The mechanical behavior of artificial leather specimens under uniaxial extension at various tensile angles was simulated through finite element computations. The differences in mechanical response in two axisymmetric directions about the main direction of the fiber family were captured, breaking through the limitations of the currently applied fiber dispersion models. …”
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Full-Wave Analysis of the Shielding Effectiveness of Thin Graphene Sheets with the 3D Unidirectionally Collocated HIE-FDTD Method by Arne Van Londersele, Daniël De Zutter, Dries Vande Ginste

“…Graphene-based electrical components are inherently multiscale, which poses a real challenge for finite-difference time-domain (FDTD) solvers due to the stringent time step upper bound. …”
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Research on Newton-Krylov Method for Multi-component Flow Heat Transfer Coupled System of High-temperature Gas-cooled Reactor by TANG Huanran, ZHANG Han, LIU Lixun, PENG Xinru, WU Yingjie, GUO Jiong, LI Fu

“…In this paper, a multi-component gas flow coupling calculation program for the characteristics of HTGRs was developed based on NK method. Among the two variants of the NK method, finite-Difference Jacobian Newton-Krylov method (DJNK) which explicitly constructs the Jacobian was chosen as the solution method. …”

Simulation of a Custom-Made Temporomandibular Joint—An Academic View on an Industrial Workflow by Annchristin Andres, Kerstin Wickert, Elena Gneiting, Franziska Binmoeller, Stefan Diebels, Michael Roland

“…In this study, we compare two finite element method-based simulation workflows from both academic and industrial perspectives, focusing on a patient-specific case involving a custom-made temporomandibular joint prosthesis. …”
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DEVELOPMENT OF A DISCRETE MATHEMATICAL MODEL OF THE HYDROTREATING DIESEL FUEL REACTOR by Ksenia Igorevna Netsvetaeva

“…The article gives an example of the transformation of the initial mathematical model of the hydrotreating diesel fuel reactor which is a system of algebraic equations into its discrete analogue, using the method of "nets" (finite difference method). The transformation of the original system was made because of the complexity of solving it explicitly and the need to obtain the most accurate values of the variables.…”
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The study of seismic resistance of rubber-metal supports by G.A. Dzhinchvelashvili, O.V. Mkrtychev

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A numerical framework for simulating fluid-structure interaction phenomena by A. De Rosis, S. de Miranda, C. Burrafato, F. Ubertini

“…The lattice Boltzmann method is used to compute fluid dynamics, while the corotational finite element formulation together with the Time Discontinuous Galerkin method are adopted to predict structure dynamics. …”
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Simulation Analysis of the Dynamic Performance of Multi Tooth Meshing of Filtering Reducer based on ANSYS- LS / DYNA by Lei Xiaochun, Yang Rongsong, Zhu Bingfeng, Liu Qiang, Chen Zhiliang

“…The filtering reducer structure principle and multi tooth elastic meshing effect are introduced,with the help of explicit dynamics software ANSYS / LS- DYNA,the three- dimensional nonlinear finite element contact analysis model is established,the dynamic meshing simulation of gear transmission mechanism under a certain speed and different load torque is carried out,the tooth surface contact stress,tooth root bending stress distribution and the rules of contact force changes under the condition of multi tooth contact with time are obtained,a theoretical basis for further filter reducer gear strength analysis and fatigue life calculation is provided by this method.…”
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Numerical Simulations for the Space-Time Variable Order Nonlinear Fractional Wave Equation by Nasser Hassan Sweilam, Taghreed Abdul Rahman Assiri

“…The explicit finite-difference method for solving variable order fractional space-time wave equation with a nonlinear source term is considered. …”
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NUMERICAL MODELING OF HYDRODYNAMIC PROCESSES IN AQUIFERS by Maxim Alexandrovich Sixtus

“…The mathematical model of the object is represented as a system of differential equations in partial derivatives that can be solved by the explicit scheme of finite difference method. Geometric parameters of the object are described by functions of two variables, it is a distinctive feature ofproposed method of mathematical modeling. …”
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Study on the Effect of the Groove Surface on Clutch Engagement Character by Chai Mengjiang

“…Based on the transient dynamics principle,a finite element model of a friction clutch system is established by using explicit dynamics method of software ABAQUS. …”
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Implicit analysis of the transient water flow with dissolved air by J. Twyman

“…The implicit finite-difference method (IFDM) for solving a system that transports water with dissolved air using a fixed (or variable) rectangular space-time mesh defined by the specified time step method is applied. …”
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Unified Description of the Mechanical Properties of Typical Marine Soil and Its Application by Yongqiang Li, Gang Wang, Liping Jing, Lei Zhang, Xinjun Cheng

“…This model can describe the unified behaviour of unsaturated soil and saturated soil using independent state variables and can uniquely describe the multiple mechanical properties of soils under general stress states, without changing the parameter values using the transform stress method. An effective stress-based, fully coupled, explicit finite element–finite difference method was established based on this model and three-phase field theory. …”
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Research on Collapse Process of Cable-Stayed Bridges under Strong Seismic Excitations by Xuewei Wang, Bing Zhu, Shengai Cui

“…In order to present the collapse process and failure mechanism of long-span cable-stayed bridges under strong seismic excitations, a rail-cum-road steel truss cable-stayed bridge was selected as engineering background, the collapse failure numerical model of the cable-stayed bridge was established based on the explicit dynamic finite element method (FEM), and the whole collapse process of the cable-stayed bridge was analyzed and studied with three different seismic waves acted in the horizontal longitudinal direction, respectively. …”
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A numerical investigation of non-rotational, rigid spherical particle sedimentation problem in viscous fluid by Nguyen Hong Phan, Nguyen Van Diep

“…Here a numerical solution of non-stationary sedimentation process is obtained by using the explicit finite difference method. The obtained results show that this model can be used for qualitative study of physical phenomenon of sedimentation problem. …”
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